On the development of regionalization relationships for lumped watershed models: The impact of ignoring sub-basin scale variability

Lumped precipitation-runoff models represent the watershed as a single, homogeneous unit, thereby ignoring spatial variability in forcing inputs and physical properties. In spite of this, spatially distributed models, which account for the variability of such factors, generally do not provide better simulations of catchment outlet runoff. This is at least in part because lumped models are easier to calibrate. However, it is often unclear whether the optimal (calibrated) parameters of a lumped model take on values that are consistent with underlying physical properties. In this study we explore the hypothesis that optimized lumped parameters are "contaminated" by noise due to the lumped representation of the watershed. We conduct a series of virtual experiments in which a daily time-step conceptual precipitation-runoff model is applied, with both lumped and distributed spatial discretizations, to 49 Austrian mesoscale basins. The experiments examine the impacts of different degrees of spatial variability in the inputs and physical properties, as well as varying complexity of the model structure. The usage of lumped models results in optimal parameters that include a considerable degree of noise, because the parameters implicitly compensate for the deficiencies in the spatial discretization. Most of the noise is attributable to neglecting the spatial variability in the physical properties, while the spatial variability of the inputs is of less importance. Further, the noise increases with system complexity, where parameter interactions significantly magnify the noise. This noise in the lumped parameters diminishes the correlation with catchment properties, even when a theoretically strong relationship exists, thereby complicating parameter regionalization as used, for example, for prediction in ungauged basins.